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In this project, the authors enhanced their ability to numerically simulate bounded plasmas that are dominated by low-frequency electric and magnetic fields. They moved towards this goal in several ways; they are now in a position to play significant roles in the modeling of low-frequency electromagnetic plasmas in several new industrial applications. They have significantly increased their facility with the computational methods invented to solve the low frequency limit of Maxwell`s equations (DiPeso, Hewett, accepted, J. Comp. Phys., 1993). This low frequency model is called the Streamlined Darwin Field model (SDF, Hewett, Larson, and Doss, J. Comp. Phys., 1992) has now been implemented in a fully non-neutral SDF code BEAGLE (Larson, Ph.D. dissertation, 1993) and has further extended to the quasi-neutral limit (DiPeso, Hewett, Comp. Phys. Comm., 1993). In addition, they have resurrected the quasi-neutral, zero-electron-inertia model (ZMR) and began the task of incorporating internal boundary conditions into this model that have the flexibility of those in GYMNOS, a magnetostatic code now used in ion source work (Hewett, Chen, ICF Quarterly Report, July--September, 1993). Finally, near the end of this project, they invented a new type of banded matrix solver that can be implemented on a massively parallel computer -- more » thus opening the door for the use of all their ADI schemes on these new computer architecture`s (Mattor, Williams, Hewett, submitted to Parallel Computing, 1993). « less

A multidimensional hybrid simulation model has been developed for use in studying plasma phenomena on extended time and distance scales. The model makes fundamental use of the small Debye length or quasineutrality assumption. The ions are modeled by particle-in-cell techniques, while the electrons are considered a collision-dominated fluid. Some electron inertial effects are retained. The fields are calculated in the nonradiative Darwin limit. The quasineutral counterpart of Poisson's equation is obtained by first summing the electron and ion momentum equations and then taking the quasineutral limit. The resulting elliptic equation correctly includes those electrostatic potentials which occur in sheath or ambipolar phenomena while neglecting the short-range electrostatic fields which give rise to plasma oscillations. This model has been implemented in a two-dimensional code QN2. A lower hybrid drift unstable equilibrium with parameters accessible to both hybrid and full-particle simulation has been selected as a test of the code and a demonstration of the model. Initial results indicate quite good agreement between the two simulation methods in linear growth rate and wave number.

The numerical time integration of an initial value problem based upon the nonlinear Vlasov equation as applied to an axisymmetric, inhomogeneous plasma column has been developed. All six components of the electric and magnetic fields are advanced self-consistently in time. An assumption has been made which neglects purely electromagnetic modes. Each field contains a contribution from plasma source terms calculated by a Green's function technique as well as a boundary value contribution which may be time dependent. The Vlasov equation has been reduced to a convenient numerical form by an extension of the standard Fourier-Hermite expansion. Radial dependence is discretized. Results are presented on the streaming instability of the electrostatic column.